CAT 2020 Question Paper With Answers & Explanation
LRDI
Question Numbers (27 to 30): Answer the questions
on the basis of the information given below.
Twenty five coloured beads are to be arranged in a grid
comprising of five rows and five columns. Each cell in
the grid must contain exactly one bead. Each bead is
coloured either Red, Blue or Green.
While arranging the beads along any of the five rows or
along any of the five columns, the rules given below are
to be followed:
1. Two adjacent beads along the same row or column
are always of different colours.
2. There is at least one Green bead between any two
Blue beads along the same row or column.
3. There is at least one Blue and at least one Green
bead between any two Red beads along the same
row or column.
Every unique, complete arrangement of twenty five beads
is called a configuration.
Q. 1 The total number of possible configurations using
beads of only two colours is:
Q. 4 Two Red beads have been placed in ‘second row,
third column’ and ‘third row, second column’. How
many more Red beads can be placed so as to
maximise the number of Red beads used in the
configuration?
Question Numbers (31 to 34): Answer the questions
on the basis of the information given below.
A shopping mall has a large basement parking lot with
parking slots painted in it along a single row. These
slots are quite narrow; a compact car can fit in a single
slot but an SUV requires two slots. When a car arrives,
the parking attendant guides the car to the first available
slot from the beginning of the row into which the car can
fit.
For our purpose, cars are numbered according to the
order in which they arrive at the lot. For example, the
first car to arrive is given a number 1, the second a
number 2, and so on. This numbering does not indicate
whether a car is a compact or an SUV. The configuration
of a parking lot is a sequence of the car numbers in
each slot. Each single vacant slot is represented by
letter V.
For instance, suppose cars numbered 1 through 5 arrive
and park, where cars 1, 3 and 5 are compact cars and
2 and 4 are SUVs. At this point, the parking lot would
be described by the sequence 1, 2, 3, 4, 5. If cars 2 and
5 now vacate their slots, the parking lot would now be
described as 1, V, V, 3, 4. If a compact car (numbered
6) arrives subsequently followed by an SUV (numbered
7), the parking lot would be described by the sequence
1, 6, V, 3, 4, 7.
Answer the following questions INDEPENDENTLY of
each other.
Q. 5 Initially cars numbered 1, 2, 3, and 4 arrive among
which 1 and 4 are SUVs while 2 and 3 are compact
cars. Car 1 then leaves, followed by the arrivals of
car 5 (a compact car) and car 6 (an SUV). Car 4
then leaves. Then car 7 (an SUV) and car 8
(a compact car) arrive. At this moment, which among
the following numbered car is parked next to car 3?
According to the question, cars 1, 4, 6 and 7 are
SUVs and cars 2, 3, 5 and 8 are compact cars.
Now, their arrival and departure are described in
the following steps.
I. 1, 2, 3, 4
II. V, V, 2, 3, 4
III. 5, V, 2, 3, 4
IV. 5, V, 2, 3, 4, 6
V. 5, V, 2, 3, V, V, 6
VI. 5, V, 2, 3, 7, 6
VII. 5, 8, 2, 3, 7, 6
Clearly, car 7 is parked next to car 3.
Q. 6 Suppose eight cars have arrived, of which two have
left. Also suppose that car 4 is a compact and car 7
is an SUV. Which of the following is a POSSIBLE
current configuration of the parking lot?
Option 1 is not possible as car 7 cannot be parked
between car 3 and car 5 because car 7 is an SUV.
Option 2 is not possible as car 6 cannot be parked
just before car 5 because 4th slot is vacant and
car 4 is a compact car. Option 3 is also not possible
as car 7 which is an SUV cannot be parked
between car 5 and car 6.
Option 4 is the possible current configuration of
the parking lot (Car 1 and car 4 have left and in
place of car 1, car 8 then arrived in that slot)
Q. 7 Suppose the sequence at some point of time is 4, 5,
6, V, 3. Which of the following is NOT necessarily
true?
Seeing the sequence: 4, 5, 6, V, 3, we can
conclude that car 1 and car 2 are definitely SUVs
which occupied two slots each. After that car 4,
car 5 and car 6 arrived and one slot is vacant which
clearly means car 4 and car 5 are compact cars.
We cannot say about the type of car 3 so option 4
is not necessarily true.
Q. 8 Suppose that car 4 is not the first car to leave and
that the sequence at a time between the arrival of
the car 7 and car 8 is V, 7, 3, 6, 5. Then which of the
following statements MUST be false?
Question Numbers (35 to 40): Answer the questions
on the basis of the information given below.
The Humanities department of a college is planning to
organize eight seminars, one for each of the eight
doctoral students - A, B, C, D, E, F, G and H. Four of
them are from Economics, three from Sociology and
one from Anthropology department. Each student is
guided by one among P, Q, R, S and T. Two students
are guided by each of P, R and T, while one student is
guided by each of Q and S. Each student is guided by
a guide belonging to their department.
Each seminar is to be scheduled in one of four
consecutive 30-minute slots starting at 9:00 am, 9:30
am, 10:00 am and 10:30 am on the same day. More
than one seminars can be scheduled in a slot, provided
the guide is free. Only three rooms are available and
hence at the most three seminars can be scheduled in
a slot. Students who are guided by the same guide must
be scheduled in consecutive slots.
The following additional facts are also known.
1. Seminars by students from Economics are
scheduled in each of the four slots.
2. A’s is the only seminar that is scheduled at 10:00
am. A is guided by R.
3. F is an Anthropology student whose seminar is
scheduled at 10:30 am.
4. The seminar of a Sociology student is scheduled
at 9:00 am.
5. B and G are both Sociology students, whose
seminars are scheduled in the same slot. The
seminar of an Economics student, who is guided
by T, is also scheduled in the same slot.
6. P, who is guiding both B and C, has students
scheduled in the first two slots.
7. A and G are scheduled in two consecutive slots.
Q. 9 Which one of the following statements is true?
Q. 12 If D is scheduled in a slot later than Q's, then which
of the following two statement(s) is(are) true?
(i) E and H are guided by T.
(ii) G is guided by Q.
Question Numbers (41 to 46): Answer the questions
on the basis of the information given below.
In an election several candidates contested for a
constituency. In any constituency, the winning candidate
was the one who polled the highest number of votes,
the first runner up was the one who polled the second
highest number of votes, the second runner up was the
one who polled the third highest number of votes, and
so on. There were no ties (in terms of number of votes
polled by the candidates) in any of the constituencies
in this election.
In an electoral system, a security deposit is the sum of
money that a candidate is required to pay to the election
commission before he or she is permitted to contest.
Only the defeated candidates (i.e., one who is not the
winning candidate) who fail to secure more than one
sixth of the valid votes polled in the constituency, lose
their security deposits.
The following table provides some incomplete information
about votes polled in four constituencies: A, B, C and
D, in this election.
The following additional facts are known:
1. The first runner up polled 10,000 more votes than the second runner up in constituency A.
2. None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled
by any pair of candidates in this constituency was at least 10,000.
3. The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the
candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the
valid votes.
Q. 15 What is the percentage of votes polled in total by all
the candidates who lost their security deposits while
contesting for constituency A?
Q. 19 The winning margin of a constituency is defined as
the difference of votes polled by the winner and that
of the first runner up. Which of the following CANNOT
be the list of constituencies, in increasing order of
winning margin?
Q. 20 For all the four constituencies taken together, what
was the approximate number of votes polled by all
the candidates who lost their security deposit
expressed as a percentage of the total valid votes
from these four constituencies?
Question Numbers (47 to 50): Answer the questions on the basis of the information given below.
A chain of departmental stores has outlets in Delhi, Mumbai, Bengaluru and Kolkata. The sales are categorized by its
three departments – ‘Apparel’, ‘Electronics’, and ‘HomeDecor’. An Accountant has been asked to prepare a summary
of the 2018 and 2019 sales amounts for an internal report. He has collated partial information and prepared the
following table.
The following additional information is known.
1. The sales amounts in the Apparel departments were
the same for Delhi and Kolkata in 2018.
2. The sales amounts in the Apparel departments were
the same for Mumbai and Bengaluru in 2018. This
sales amount matched the sales amount in the
Apparel department for Delhi in 2019.
3. The sales amounts in the HomeDecor departments
were the same for Mumbai and Kolkata in 2018.
4. The sum of the sales amounts of four Electronics
departments increased by the same amount as the
sum of the sales amounts of four Apparel
departments from 2018 to 2019.
5. The total sales amounts of the four HomeDecor
departments increased by Rs 70 Crores from 2018
to 2019.
6. The sales amounts in the HomeDecor departments
of Delhi and Bengaluru each increased by Rs 20
Crores from 2018 to 2019.
7. The sales amounts in the Apparel departments of
Delhi and Bengaluru each increased by the same
amount in 2019 from 2018. The sales amounts in
the Apparel departments of Mumbai and Kolkata also
each increased by the same amount in 2019 from
2018.
8. The sales amounts in the Apparel departments of
Delhi, Kolkata and Bengaluru in 2019 followed an
Arithmetic Progression.
Q. 21 In HomeDecor departments of which cities were the
sales amounts the highest in 2018 and 2019,
respectively?
Q. 23 Among all the 12 departments (i.e., the 3 departments
in each of the 4 cities), what was the maximum
percentage increase in sales amount from 2018 to
2019?
